Shrinkwrap tetris shapes without scaling or diagonal shapes
Avoid Boolean whenever possible. For such simple shapes you should not need any "merging" , proper topology is important especially if you are deforming shapes where constant mesh density is helpful.

If you just want the morph into a sphere use the Cast modifier instead, it yields cleaner results.

Model the shape by extruding two faces of a default cube, then add a Subsurf modifier set to Simple to give it geometry to work with, followed by the Cast modifier set to Sphere. Control progression from the Factor slider.